A question that my students frequently ask me is: “Is 0 even or odd or both?”
To answer this question, we first need to define what “even” means:
An even number is a number n which can be written as n=2⋅k for a whole number k. That means if we divide an even number by two, there is no remainder left.
Is 0 Even?
An even number in mathematics is a number that can be written as n=2⋅k for a whole number k. If k=0, the equation 0=2⋅k remains accurate. This makes 0 an even number.
Can we write 0=2⋅k for some k? Yep, we can if we choose k=0.
That means that zero is even.
Is 0 Also Odd?
Again, we first need to define what “odd” means. The common definition is very similar to the definition of even.
An odd number is a number n which can be written as n=2⋅k+1 for a whole number k.
Can we write 0=2⋅k+1 for some whole number k? Nope. We can’t because solving this equation for k yields k=-1/2,which is not a whole number.
Is 0 Even? Answered.
Alright, the proof is done. Zero is even and only even. And it isn’t even (pun intended) too difficult, is it?
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